Understanding Decimal Notation
Date: 06/10/2002 at 00:03:37 From: Sharon Brown Subject: Decimals I have read your decimal page. I need to understand how the following problems can be worked out step by step. I need to see this process so it will stick in my head. 9/10 = 0.9 Why? How should it be worked out? 12 15/100 = 12.15 0.7 = 7/10 2.50 = 2 50/100 The explanation I was given is that you should be able to look at these and work them out. I need to understand the process. Please help! Thanks
Date: 06/10/2002 at 11:58:03 From: Doctor Ian Subject: Re: Decimals Hi Sharon, When we write a number using decimal notation, it's really an implied sum. That is, the notation '342.15' is really just a very compact way of writing the sum 3*100 + 4*10 + 2*1 + 1*(1/10) + 5*(1/100) That's what we _mean_ when we cram all those digits together in that order. Note that each term in the sum is a single digit multiplied by a power of 10: 2 1 0 -1 -2 3*10 + 4*10 + 2*10 + 1*10 + 5*10 If you're not sure how exponents work (especially zero and negative exponents), you might want to take a few minutes to look at this: Properties of Exponents http://mathforum.org/library/drmath/view/57293.html Now, the nice thing about the fractional part is that we can change between powers of 10 just by adding and taking away zeros, so 1 5 10 5 15 -- + --- = --- + --- = --- 10 100 100 100 100 So when you want to convert between decimals and fractions, all you have to do is find the power of 10 corresponding to the last digit, and then treat the others as an integer, e.g., 1 2.1 -> 2 + --- 1 10 <-- 10 4456 12.4456 -> 12 + ---- 4 10 <-- 10000 The shortcut is to count the number of decimal places, and put the same number of zeros after the 1 in the denominator: 56 3.0056 -> 3 + ----- 10000 ^ ^ | | 4 decimal 4 zeros places But instead of trying to memorize the shortcut, you're better off making sure that you understand why it works, so that if you ever forget it, you can figure it out again on your own. (In general, the best way to find out whether you understand something is to try to explain it to someone else who doesn't understand it.) Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 06/11/2002 at 22:33:52 From: Sharon Brown Subject: Thank you (Decimals) Ian, Thanks again for your help.
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